PGDBA2019 Related Question Answers
1.
Answer the questions based on the following information.
The following bar diagram represents the number of daily wages (in rupees) of 100 labourers in different wage classes on a construction site. Here the class interval a-b includes all wages (in rupees) greater than or equal to a and less than b except for the interval 360-400, where both the end points are included. No.of labourers 
Wages in RupeesThe number of labourers receiving at least 320 is:
3. The maximum wage (in Rupees), such that at least 50% of the labourers definitely earn more than that, is
4.
Answer the questions based on the following information.
The following table gives month-wise arrivals of foreign tourists in India in the years 2016 & 2017.
Table: Month-wise Arrivals of Foreign Tourists (in Thousands) in India (2016-2017) 
In which month of 2017 is the percentage increase over the corresponding month of the previous year the minimum?
7. If the system of linear equations $$2x+ y+7z = a$$ $$6x-2y+11z = b$$ $$2x-y+3z = c$$ has infinite number of solutions, then $$a, b, c$$ must satisfy
8. If $$\alpha, \beta$$ are the roots of the equation $$x^2 + 3x - 3$$ , then the value of $$(\alpha + 1)^{-1} + (\beta +1)^{-1}$$ is equal to
9. The number of real roots of the equation $$(e^x + e^{-x})^3 + 3(e^x + e^{-x})^2 + 3(e^x + e^{-x}) = 7$$
10. Let $$x = -\frac{1}{1!}\cdot\frac{3}{4} + \frac{1}{2!}\cdot(\frac{3}{4})^2 -\frac{1}{3!}\cdot(\frac{3}{4})^3 +$$.... and $$y = x - \frac{x^2}{2} + \frac{x^3}{3} - $$..... then the value of y is
11. If $$P, Q, R$$ are subsets of some universal set, then the conditions $$P^c \cap Q \subseteq R^c \cap Q$$ and $$P^c \cap Q^c \subseteq R^c \cap Q^c$$ imply
12. The sides of triangle are 3 consecutive even integers with the largest side being less than 13. What is the total number of such triangles?
13. The circle $$x^2 + y^2 = 9$$ intersects with the parabola $$y^2 = 8x$$ at a point P in the fin quadrant. The acute angle between the tangents to the circle and the parabola at the point P is
14. The interior angles of a convex polygon are in arithmetic progression. The smallest angle is 120° and the common difference is 5°. Then the number of its sides is
17. All words formed by permutations of the word `WARE' are arranged in a list according to the dictionary ordering. The position of the word 'WEAR' in this list is at number
18. The number of integers between 300 and 1100 which ar divisible by either 7 or 13 but not both is
19. The diameter of the circumcircle of the triangle formed by the line $$24x + 7y =168$$ and the coordinate axes is
20. Let $$f: R \rightarrow R$$ be an even function that is differentiable every where except exactly at 10 distinct points. Then which of the following statements is TRUE?
21. Let the function $$f$$ be defined on the set of real numbers by $$ f(x) = \begin{cases}x^2 - x, & if x < 1\\\frac{x^2 - 1}{3}, &if x \geq 1\end{cases}$$ then which of the following statement is TRUE ?
22. If $$f'(x)$$ and $$g'(x)$$ exist for all $$x \in R$$, and if $$f'(x)>g'(x)$$ for all $$x \in R$$, then the curve $$y = f(x)$$ and $$y = g(x)$$ in the $$xy$$-plane
23. The value of the integral $$\int_{-\frac{1}{\sqrt{3}}}^{\frac{1}{\sqrt{3}}} (\frac{x^2 - \tan x}{1 + x^2})dx$$ is equal to
25. Let $$[x]$$ denote the greatest integer less than or equal to $$x$$. The value of the integral $$\int_{0}^{\sqrt{2}} [x^2]e^x dx$$ is equal to
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